A pet store has 9 puppies, including 3 poodles, 2 terriers, and 4 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random with replacement (they may both select the same one), find the probability that they both select a poodle. The probability is (Type an integer or a simplified fraction.)

Step 1 ：The total number of puppies in the pet store is 9, including 3 poodles, 2 terriers, and 4 retrievers.

Step 2 ：Rebecka and Aaron, in that order, each select one puppy at random with replacement. This means they may both select the same one.

Step 3 ：We want to find the probability that they both select a poodle.

Step 4 ：The probability of an event is calculated by dividing the number of ways the event can occur by the total number of outcomes. In this case, the event is both Rebecka and Aaron selecting a poodle, and the total number of outcomes is the total number of puppies.

Step 5 ：Since the selection is with replacement, the total number of outcomes remains the same for both selections.

Step 6 ：The probability of Rebecka selecting a poodle is \(\frac{3}{9} = 0.3333333333333333\)

Step 7 ：The probability of Aaron selecting a poodle is also \(\frac{3}{9} = 0.3333333333333333\) because the selection is with replacement.

Step 8 ：The probability of both Rebecka and Aaron selecting a poodle is the product of the individual probabilities, which is \(0.3333333333333333 \times 0.3333333333333333 = 0.1111111111111111\)

Step 9 ：Final Answer: The probability that both Rebecka and Aaron select a poodle is \(\boxed{\frac{1}{9}}\).